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A 3-Component fiber-optic accelerometer array for well logging M. Pang, L.W. Wang, M. Zhang, H.P Zhou and Y.B. Liao Department of Electronic Engineering, Tsinghua University, Beijing 100084, China E-mail: [email protected] Tel: (8610)-6278-1372

Fax: (8610)-6277-0317

Abstract：A 3-Component fiber-optic accelerometer (FOA) array used in oil-well logging is presented. A novel and general parameter ( SB 2 D −1P ) to evaluate the characteristics of the interferometric FOA is brought forward.

1.

Introduction

The technology of modern vibration sensors is well developed and a broad range of different specifications for various applications are currently available. Nevertheless, in some special cases fiber-optic sensors may offer distinct advantages [1]. In the applications of fiber-optic technology to sensor system, the interferometer takes a very important position because of its high sensitivity. Some kinds of FOA based on compliant cylinder or based on flexural dish with large sensitivity have been presented. A FOA based on compliant cylinder with the sensitivity: 2.7 × 103 rad / g , bandwidth: 100Hz and dimension: 10.25mm is shown in [2], and a typical FOA based on flexural disk that has been presented in [3] has the sensitivity: 12.25rad / g , bandwidth: 2kHz, dimension: 30mm, but both of them didn’t demonstrate the correlation of them. For an applied FOA the three performance parameters: phase shift sensitivity, 3dB bandwidth, and the configuration dimension are very important and all of them correlate with each other. So how to select the parameters simply and quickly is an essential problem in the design of FOA. In order to apply the fiber-optic sensor in the well logging, all these parameters should be considered comprehensively. So analyzing the relationships of these performance parameters of the FOA becomes necessary. Using the rule of correlation, the performance parameters of the FOA can be adjusted to suit different applied occasions. 2.

Sensor theory

The configuration of the FOA is shown in Fig.1.

Fig. 1. The configuration of the FOA and its signal processing algorithm

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The phase shift sensitivity of the FOA based on pull-push compliant cylinders is given by equation (1) [2]. S=

8π 2η Rσ (1 − Pc ) M × λd f X keff

(1)

From the mass-spring dynamics model of accelerometers, the 3dB bandwidth is given by equation (2).

B3dB =

δωn δ = 2π 2π

δ = 1 − 2ξ 2 −

2keff M

(2)

2 − 16ξ + 16ξ 2 2

4

Where R is the outer radius of the compliant cylinder, it can be seen as a characteristic dimension parameter of the sensor, H is the height of the compliant cylinder, M is the mass of mass load,

ξ

is the damping coefficient.

In order to the minimize the interaction of the parameters ( S , B3dB and R ) we define a novel parameter ( SB 2 D −1P ) which is given by equation (3) to evaluate the capability of the FOA. SB 2 D −1P = X = 1−

Where,

λ

S × B32dB 4ησ (1 − Pc ) δ 1/ 2 = × R λd f X

(3)

R2 r2 (2σ 2 − 1) − 2 2 + σ ] 2 HER R − r R −r

K fn N

[

2

is the wavelength of the laser,

η

is the refractive index of the fiber, d f is the diameter of sensing

fiber, Pc is the Pockels coefficient of the fiber core material, E is Young’s modulus of the compliant cylinder material,

σ

is the Poisson ratio and K fn is the normalized fiber stiffness. When sensing fiber and the material of compliant

1/ 2 cylinder are fixed, all of them are constants. Although the value of δ can be improved by using some special

X

methods, its potential is finite. Using this rule, it can be seen that when the dimensions of the accelerometers are fixed, the increase of the phase shift sensitivity by using weightier mass load or decreasing the stiffness of the compliant cylinder must result in the narrowing of the bandwidth. And if a FOA of the same type with larger phase-shift sensitivity as well as broader bandwidth is needed, the only thing that can be done is to change the configuration or dimensions of the accelerometer. So the parameter SB 2 D −1P actually reflects the capability limitation of the FOA based on compliant cylinders. Because almost all the accelerometers use the mass-spring system as their dynamics models and the only difference is that they converts the micro-distortion into different kinds of parameters to measure, this SB 2 D −1P can also be used to guide the designs of the FOA of other types. 3. Experimental setup and results k In experiments, a range of accelerometers with different M and eff are made, and their design-parameters and

performances are shown in Table. 1. Table. 1. The design parameters, performances

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2 −1 2 −1 In Table.(1), we can see that SB D P of those five FOAs have the same order, and the SB D P of NO.1

accelerometer has a larger value because it has low X and high mass ratio ( M ), where m is the mass of the m

compliant cylinder. In the practical systems we used the FOA with the same parameters as NO.1. Its main/cross sensitivity as a function of vibration frequency is demonstrated in Fig.2 (1), and Fig.2 (2) shows the detected optical phase shift versus acceleration when the vibration frequency is 100Hz. Within the bandwidth of the accelerometer, the cross sensitivity is lower than the main sensitivity by 5%~10%@10~500Hz.

(1)

(2)

Fig. 2 (1) Main/Cross sensitivity of accelerometer NO.1 as a function of vibration frequency Fig. 2 (2) The detected optical phase shift versus acceleration (f=100Hz) In the field experiments, the accelerometer array has four sensor stages and each of the stages consist of three FOAs which are fixed in three orthogonal directions. The photographs of the accelerometer array are shown in Fig. 3.

Fig. 3. Photographs of the accelerometer array

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In Fig. 3, the photograph ① shows the four sensor stages which are assembled together. Each of them contains two parts: one is the push-lean part whose duty is to adjust the location of the sensor part and make it stick to the wall of the oil-well firmly; the other part is the sensor-part which is shown in the photographs ② and ③. The four-stage accelerometer array has been tested in a well at Huabei oil field of China on October in 2005. It was sent into the oil well to about 1 km depth. An explosive gun was used to simulate the shake source. A group of seismic signal detected by the accelerometer array is shown in Fig. 4. The seismic wave first reached sensor-stage 1, then stage the sensor-stages 2~4 in turn. All the four stages have the same spacing intervals. In Fig. 4 the spots with which they time intervals of the seismic signal are measured is pointed out, they are respectively at time-spots: 2952, 2967, 2981 and 2995.

Fig. 4. The setup and results of experiments at Huabei oil field 4.

Conclusion

In summary, we analyzed the relationships of three important performance parameters ( S , B3dB and R ) and then brought forward a new evaluation parameter SB 2 D −1P to guide the design of FOA. A 3-Component FOA array used in oil well logging were presented. By multiplexing three orthogonal unidirectional elements, the array can obtain the three components of the vibration signal at different depth simultaneously. The output signal and the acceleration to be measured exhibit a good linear relationship. The accelerometer also shows good stability and consistency, and can work in high temperature condition. Field experimental results indicate that the main-sensitivity, cross-sensitivity, bandwidth and minimum detectable level are 24.5 rad/g, 5%~10% @10~500Hz, 10~900Hz and 50 μg/Hz1/2 respectively. References 1

J.Dakin, B.Culshaw, Optical Fiber Sensors: Principle and Components, Artech House, Boston, 1989.

2

Pechstedt R D, and Jackson D A. Design of a compliant-cylinder-type fiberoptic accelerometer: theory and experiment. Applied Optics. 1995,

34(16): 3009-3017 3

Geoffrey G A, and Nash P J. High-responsivity fiber-optic flexural disk accelerometers. Journal of Lightwave Technology. 2000, 18(9):

1233-1243 4

Dandridge A, Tveten A B, and Giallorenzi T G. Homodyne demodulation scheme for fibre-optic sensors using phase generated carrier, IEEE

Journal of Quantum Electronics. 1982, QE-18: 1647-1653 5

J.H. Lin, N.S. Qu, H.C. Sun. Calculational Structural Mechanics, Higher Education Press, Beijing, 1989(in Chinese).